Radiographic imaging, in its simplest expression, is an X-ray beam traversing an object and a detector relating the overall attenuation per ray. The attenuation is derived from a comparison of the same ray with and without the presence of the object. From this conceptual definition, several steps are required to properly construct an image. For instance, the finite size of the X-ray generator, the nature and shape of the filter blocking the very low energy X-ray from the generator, the details of the geometry and characteristics of the detector, and the capacity of the acquisition system are all elements that affect how the actual reconstruction is performed. In the reconstruction, the map of the linear attenuation coefficient (LAC) of the imaged subjects is obtained from the line integrals of the LAC through an inverse Radon transform. The line integrals can be related to the logarithm of the primary intensity of the X-rays passing through the subject. However, the measured X-ray intensity on detector may include both scattering photons and primary photons. Thus, the images reconstructed from scattering, contaminated intensities may contain some scattering artifacts.
In one of many possible geometries, the X-ray source on top of the graph shown in FIG. 1 is emitting a X-ray beam forming a fan, traversing the object. While a wide range of values can exist, typically, the distance “C” is around 100 cm, “B” is around 60 cm, and “A” is around 40 cm. The principle of tomography requires that each point of the object is traversed by a collection of rays covering at least 180 degrees. Thus, the entire X-ray generator and detector assembly will rotate around the patient. Mathematical considerations show that the tomographic conditions are met when a scan of 180 degrees plus the fan angle is performed.
In addition to the details of the scanner geometry and the detector behavior, the very nature of the X-ray interaction with the matter it traverses makes the problem more complex and requires another layer of correction and compensation.
For example, scattering is one of the major sources of discrepancy between the expected attenuation behavior and the measured data from a scanner without an anti-scatter grid or with a non-perfect anti-scatter grid. The naïve assumption that all the measured photons originate directly from the X-ray source is not exactly true. X-ray photons can be diverted from their original course in a purely elastic collision (Rayleigh scattering) or in a more complex inelastic collision (Compton scattering) in which both direction and energy are affected.
The prevalence of each mode of interaction is highly dependent on the energy of the X-ray and the nature of the medium. Typically, the relative ratio follows the behavior shown in FIG. 2, which shows the attenuation coefficient as a function of energy of the X-ray for photoelectric, Compton, and Rayleigh collisions.
The angle at which the resulting Compton photon will be diverted is also highly dependent on the energy of the incident X-ray. This relationship is described by the Klein-Nishina equation and result in a progressively more forward collision as the energy of the photon increases. As shown in FIG. 3, the outer curve corresponds to a low-energy photon in which almost all angles are possible, while the inner curves shows a clear preference for the forward direction.
The end result is that the detector measures the attenuated X-ray beam plus the scattered radiation. The relationship between the measured radiation and the attenuating nature of the object is therefore more complex.
In the photon energy range of medical imaging, e.g., 20 keV-140 keV, the major interaction processes of photons and matter are the photoelectric process and Compton scattering. Rayleigh scattering has small contribution to the total attenuation. However, the Rayleigh scattering intensity on a detector is comparable to the Compton scattering intensity because Rayleigh scattering is a forward scattering in the relevant energy range.
The cross-sections (or probability) of the photoelectric process and Compton scattering are related to the effective Z of a material. For high-Z materials, the photoelectric process is dominant and fewer Compton photons are generated. For low-Z materials, the Compton process is important and more scatter photons are generated. The Rayleigh scattering process depends on the electronic structure of the atoms, molecules, and clusters of a material and cannot be described with only a few parameters. With the material information, one can estimate the strength of Compton scattering and improve the accuracy of the scatter model.
Several systems have been proposed to address scattering contamination. For example, most modern commercial scanners include an “anti-scatter” filter. This device is a collimation system exploiting the fact that all scattered photons will be diverted from their original path and will therefore enter the detector at a different angle from the photons coming directly from the X-ray tube, which is typically a small (e.g., less than one millimeter wide) point that is on the order of one meter away. Thus, as shown in FIG. 4, a series of mechanical, attenuating fins could block radiation not emanating from the source.
Two types of collimation exist. In the one-dimensional approach shown in FIG. 5, fins are arranged along the long axis (z-axis) of the scanner to prevent scattered radiation from entering the detector in the transaxial plane. It is clear, however, that radiation can enter the detector in this design if the radiation stays in an axial plane.
It is indeed possible to build a two-dimensional array of fins that provide shielding for scattered radiation for all planes, as shown in FIG. 6. Of course, construction of such a device is not without its own complexity and cost, especially when considering that the detector elements are typically 1 mm×1 mm, sometimes even smaller. It is also to be realized that this filter, due to the fact that a finite amount of material is necessary to block the scattered radiation, will also block some of the desired, unscattered, primary beam. With strong requirements to minimize the amount of radiation required to produce a desired image, blocking “good” photons at the detector is generally not a good strategy. For this reason, the one-dimensional filter is generally preferred, but requires additional correction since, by definition, it will allow some amount of scattered radiation in the axial planes.
One of a multiple of ways to address this problem is to use a forward scatter model with a polychromatic X-ray source. In such a model, the scatter intensities are expressed as a combination of Compton scattering and Rayleigh scattering. In the scatter model, each of the scattering intensity terms is modeled as a two-dimensional convolution of a forward function and a Gaussian kernel in each view. The forward function is related to the primary intensities that can be obtained by subtracting the scatter intensities from the measured total intensities. Polychromatic factors for Rayleigh scattering and Compton scattering are included in the respective forward functions. These polychromatic factors depend on the rays through effective energy of the spectrum for the specific ray. Scatter cross sections depend on photon energy and each ray has its effective energy due to the bowtie filter for a polychromatic source. Thus, the effective energy is related to the cross sections to account for the polychromatic effect. The Gaussian kernels are derived from the differential cross-sections of Rayleigh scattering and Compton scattering. Due to the forward nature of Rayleigh scattering in the energy range of medical imaging, it is described by a narrow Gaussian kernel. The Compton process is related to the wide kernel. The effect of a one-dimensional anti-scatter filter can also be included in the kernels. For each view, an iterative procedure is adopted to obtain the primary intensities from the measured total intensities.
The disadvantage of conventional CT systems is that the reduction of scattered radiation is made at the expense of the general dose efficiency of the system, and that the compromise approach using a one-dimensional filter still relies on a series of assumptions that are sometimes not clearly met.
For example, FIGS. 7A-7E show the CT numbers for various materials as a function of the slice number for an ACT phantom. Compared with the true value, the CT numbers from the scatter correction model for air, water, and polyethylene are accurate, but the CT numbers of bone and acrylic illustrate the scatter over-correction. The over-correction can be attributed to the relatively high Z feature of bone and acrylic. High Z materials generate fewer scatter photons, but the model assumes relatively low Z material (water), which has high scatter Compton probability.